Related papers: On finiteness properties of polynomial functors
This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…
This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…
In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
We study the category of polynomial functors from finitely generated free groups to a stable infinity-category D. We show that this category is equivalent to the category of excisive functors from pointed animas to D, and also to truncated…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
We consider the relationship between the relative stable category of Benson, Iyengar, and Krause and the usual singularity category for group algebras with coefficients in a commutative noetherian ring. When the coefficient ring is…
In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…
We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative noetherian ring. In particular, we extend the isomorphism properties of certain natural morphisms from homologically…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…
The goal of this expository article, based on a lecture I gave at the 2016 ICRA, is to explain some recent applications of "categorical symmetries" in topology and algebraic geometry with an eye toward twisted commutative algebras as a…
We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.
We study the arithmetic of seminormal $v$-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global…
We show that single-variable polynomial functors over the category $\mathcal{S}$ of infinity groupoids, as defined by Gepner-Haugseng-Kock, are exactly colimits of representable copresheaves indexed by infinity groupoid. This allows us to…
Factoring ideals in integral domains is a central topic in multiplicative ideal theory. In the present paper we study monoids of ideals and consider factorizations of ideals into multiplicatively irreducible ideals. The focus is on the…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.
We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compactness. This is achieved through the concept of…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…